Efficient backward selection of k-space samples in MRI on a hexagonal grid

Certain types of magnetic resonance imaging (MRI) such as magnetic resonanc e spectroscopic imaging and three-dimensional (3D) MRI require a great deal of time to acquire the image data. The acquisition time can be reduced if the image has a limited region of support, such as when imaging the brain o r a cross section of the chest. Hexagonal sampling of the spatial frequency -domain (k-space) yields a 13.4% sampling density reduction compared to rec tangular sampling of the k-space for images with a circular region of suppo rt (ROS) without incurring spatial aliasing in the reconstructed image. How ever, certain nonuniform sampling patterns are more efficient than hexagona l sampling for the same ROS. Sequential backward selection (SBS) has been u sed in previous work to optimize a nonuniform set of k-space samples select ed from a rectangular grid. To reduce the selection time, we present SBS of samples from a hexagonal grid. A Smith normal decomposition is used to tra nsform the nonrectangular 2D discrete Fourier transform to a standard recta ngular 2D fast Fourier transform so that the spatial-domain samples are rep resented directly on a rectangular grid without interpolation. The hexagona l grid allows the SBS algorithm to begin with a smaller set of candidate sa mples so that fewer samples have to be eliminated. Simulation results show that a significantly reduced selection time can be achieved with the propos ed method in comparison with SBS on a rectangular grid.